Internal problem ID [13111]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _exact, _rational, _Bernoulli]
\[ \boxed {y^{2} x +x^{2} y y^{\prime }=6} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x*y(x)^2-6+x^2*y(x)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y = \frac {\sqrt {12 x +c_{1}}}{x} y = -\frac {\sqrt {12 x +c_{1}}}{x} \end{align*}
✓ Solution by Mathematica
Time used: 0.19 (sec). Leaf size: 38
DSolve[x*y[x]^2-6+x^2*y[x]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {12 x+c_1}}{x} y(x)\to \frac {\sqrt {12 x+c_1}}{x} \end{align*}